"Volatility still hasn't gone away," John Hailer, CEO of Natixis Global Asset Management, said. "There's a lot of volatility in this market."

But he doesn't expect a big correction since stocks are not yet overly expensive. "You might have some pullback but it doesn't mean you don't want to get into the equity markets. There still could be some run here," Hailer said.

UBS's Jeremy Zirin also pointed to the economic data as reason for the market comeback.

Paulsen: 'Trendless, Sideless Market' in Second Half

A big swing for the markets after mixed signals from the Fed on when the central bank will taper its QE program. James Paulsen, Wells Capital Management, says in the market will digest its gains in the second half of the year. Larry Lindsey, former Fed governor, also shares his thoughts.

"What probably was the trigger for the reversal today: you got better data on housing and better data on jobless claims," Zirin said. "So if the labor market is healing, if home prices are rising, you're going to see an improving economic trajectory throughout the second half of the year. And if that stronger economic growth is driving moderation in the amount of the bond purchase program from the Fed that's a net positive for markets."

Fed Uncertainty

Markets were spooked Wednesday when both Fed chairman Ben Bernanke and the minutes from the last policy setting meeting suggested the central bank may be getting closer to tapering bond purchases.

According to the Fed minutes, "a number of participants expressed willingness" to reduce quantitative easing as early as June, if economic data suggested sufficiently strong and sustained growth. However, officials differed about what evidence would be necessary, and the likelihood of it materializing.

Jan Randolph, head of sovereign risk at IHS Global, tells CNBC that the financial system is representative of two drunks: the financial markets and the real economy.

And in his Congressional testimony earlier in the day, Bernanke reiterated the central bank's intention to "maintain highly accommodative monetary policy as long as needed," adding that any near-term decision on scaling back bond purchases depended on an improvement in jobs data.

On Thursday, James Bullard, president of the Federal Reserve Bank of St. Louis, said he did not think the Fed was "that close" to starting to curtail quantitative easing, but it was the likely next step if the economy continued to improve and inflation picks up.

Landesman said the news that quantitative easing will eventually come to an end should have been more negative for markets since it shows "the Fed isn't going to be the safety net forever."

A bear, Landesman expects a correction. "I would expect this market to start correcting downward by the beginning of June," he said.

"It is not good and it does increase the chances of a sequential slowdown in the second quarter GDP [gross domestic product]. Simply put, domestic demand this time wasn't strong enough to counter fully the impact of still weak external demand," Donna Kwok, greater China economist at HSBC, told CNBC on Thursday.

A sharp selloff in Japan also kept investors on edge. Japan's benchmark Nikkei 225 fell 7.3 percent with the yen gaining ground and bond yields spiking. That was the index's biggest drop in more than two years.

"Almost everything went wrong during the day — the bond market had a bit of a crash, China PMI data, and the yen is stronger. The market is really overheated, all it's looking for is a trigger," Nicholas Smith, Japan strategist at CLSA, told CNBC.